Suppose the line contains the points (4,0) and (0,-2). If x = 3, find y.

Using properties of quadrilaterals, the value of z = 48.

A quadrilateral has four straight sides and is a two-dimensional shape.. Quadrilaterals encompass geometries of parallelograms, trapezoids, rectangles, kites, squares, and rhombuses. What four characteristics does a quadrilateral have? There are four of them. There are four of them. 360° is the total of all interior angles. There are two diagonals in them.

The supplied figure makes it obvious that x=90 degrees because it is right-angled.

The figure is a kite, thus 5y+2=42, 5y=40, and y=8 are the results.

Since it's a kite, angle B must equal angle D, thus if we take ADO produces a triangle with O as the midpoint, thus x+z+42=180, 90+42+z=180, z=180-132, z=48.

This is the concrete answer.

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3. 2 is the mean of the sampling distribution of the sample mean for samples of size 16.

Hence,

3. 2 is the mean of the sampling distribution of the sample mean for samples of size 16.

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The inverse equations are F(x)⁻¹ = 2x - 20 and F(x)⁻¹ = ( x/ 8) + ( 3 /8).

A function is defined as the expression that set up the relationship between the dependent variable and the independent variable. In an inverse function, the value of two variables x  and y are interchanged,  and then the value of y is given an inverse function.

Given that the two equations are y= 1/2X+10 and y= -8X+3. The value of  inverse functions will be calculated by replacing the x and y values and solving for y,

y = 1/2X+10

x = y / 2 + 10

y = 2x - 20

The inverse of the second equation is calculated as,

y= -8x+3

x = -8y + 3

y = x / 8 + 3 / 8

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Answer:

Step-by-step explanation:

If the half-life of nitrogen is 10 minutes, the gram that will be left out of 120 grams of nitrogen after 120minutes is 30grams

Half-life, in radioactivity is the interval of time required for one-half of the atomic nuclei of a radioactive sample to decay (change spontaneously into other nuclear species by emitting particles and energy), or, equivalently, the time interval required for the number of disintegrations per second of a radioactive.

The half life is expressed as:

half life = 0.693/decay constant

The half life of Nitrogen is 10minutes

therefore 10 minutes = 1/2 of 120grams

20minutes = 1/4 of 120 = 120/4 = 30 grams.

Therefore the mass of nitrogen atom that will left in 20minutes is 30grams

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Answer:  120

120 x 0.85 = 102

Have a good day!

Answer: 120

Step-by-step explanation: (102 x 100) / 85

An inequality can be written in two different ways depending on the desired result. In both cases, the inequality is used to represent the desired result of Mario earning no more than or more than $500.

If Mario wants to earn no more than $500:

I ≤ 500

If Mario wants to earn more than $500:

I > 500

An inequality can be written in two different ways depending on the desired result. In the first case, Mario wants to earn no more than $500. This can be written as I ≤ 500, which means "I is less than or equal to 500". The symbol ≤ indicates that the maximum value for I is 500. In the second case, Mario wants to earn more than $500. This can be written as I > 500, which means "I is greater than 500". The symbol > indicates that the minimum value for I is 500. In both cases, the inequality is used to represent the desired result of Mario earning no more than or more than $500.

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Answer:

A. Let x be the number of hours for which the companies charge the same amount.

Party Time: 100 + 50x = 175 + 25x

Let's Dance Company: 175 + 25x = 100 + 50x

B. To solve this system of equations, we can use substitution. We can start by isolating one of the variables on one side of the equation and then substitute that expression into the other equation.

x = 25

C. To show that the solution results in the same charge for both companies, we can substitute the value of x back into the equations for each company and see if they are equal.

Party Time: 100 + 50(25) = 100 + 1250 = 1350

Let's Dance Company: 175 + 25(25) = 175 + 625 = 800

1350 = 800

The two companies charge the same amount for 25 hours.

The 3/2cm unit rate corresponds to the proportional relationship shown in the graph.

What is the rate of change?

The term "rate of change" (ROC) describes the rate at which something changes over time. Thus, it is not the number of individual changes themselves but rather the acceleration or deceleration of changes (i.e., the rate). The rate of change is a tool used in finance to comprehend price returns and spot trend momentum.

Here, we have

Given: points (0, 0) and (6, 9)

The term for the rate of change is the slope.  

This means to find the unit rate, we use the formula for slope:

m = (y₂-y₁)/(x₂-x₁)

m = (9-0)/(6-0)

m = 9/6

m = 3/2cm

Hence, the 3/2cm unit rate corresponds to the proportional relationship shown in the graph.

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The distance between two opposite corners of the prism is 13.

The distance between two opposite corners of a rectangular prism can be found using the Pythagorean theorem, which states that the square of the distance between two points is equal to the sum of the squares of the distances along the two axes that are perpendicular to each other.

In this case, the two opposite corners of the prism are the top-front corner and the bottom-back corner. The distance between these two corners is the hypotenuse of a right triangle with legs of length 3 (the length of the prism), 4 (the width of the prism), and 12 (the height of the prism).

So, using the Pythagorean theorem (a² + b² = c²), the distance between two opposite corners of the top of the rectangular prism is (3² + 4² = 5²) 5.

To determine the distance between two opposite corners of the prism, get the diagonal distance of the cross section made by the two opposite corners of the top of the rectangular prism.

d² = 5² + 12²

d = 13

Hence, the distance between two opposite corners of the prism is 13.

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Yes, there are formulas in algebra. Algebra is a branch of mathematics that deals with mathematical equations and their properties. Some common formulas in algebra include the quadratic formula, the slope-intercept form of a linear equation, and the distance formula. These formulas can be used to solve a wide variety of mathematical problems involving equations and variables.

1.  (a + b)^2 = a^2 + 2ab + b^2

2.  (a - b)^2  = a^2 - 2ab + b^2

3.  (a + b) (a - b)  = a^2 - b2

4.  (x + a)(x + b)  = x^2 + (a + b)x + ab

5.  (x + a)(x - b)  = x^2 + (a - b)x - ab

6.  (x - a)(x + b)  = x^2 + (b - a)x - ab

7.  (a+b+c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)

8. a^3 + b^3 + c^3 - 3abc = (a + b + c ) ( a^2 + b^2 + c^2 – ab – bc – ca ) + 3abc

9. a^3 + b^3 + c^3 = 3abc   (if a + b + c = 0)

An expression that consists of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

With the use of mathematical expressions, algebra is the area of mathematics that helps to depict situations or problems.

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Option A. Angle A = 46.8 degrees, side A C = 1.9 meters, Side A B = 3.7 meters satisfies the conditions of the problem: angle C is 90 degrees, angle B is 43.2 degrees, and side B C is 3.2 meters.

A right triangle is a type of triangle in which one of the angles is a right angle (90 degrees). The side opposite the right angle is called the hypotenuse and is typically the longest side of the triangle.

The other two sides are called the legs and are typically shorter than the hypotenuse. The Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs, applies to all right triangles

Therefore, the remaining options (b, c, and d) do not satisfy the conditions of the problem and therefore are not correct.

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To find the number that makes the ratio 8:9 equivalent, we need to first understand the concept of equivalent ratios.Therefore, 9 is the number that makes the ratio 8:9 equivalent.

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The solution of the given quadratic equation [tex]x^{2} +5x+6[/tex] = 0 is x = -2 and -3

Now, According to the question:

What is quadratic equation?

A quadratic equation is a second-order polynomial equation in a single variable x ax2+bx+c=0. with a ≠ 0 . Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The given quadratic equation is:

[tex]x^{2} +5x+6[/tex] = 0

To solve the equation:

Comparing the above equation with the standard form of quadratic equation:

[tex]ax^{2} +bx+c=0[/tex]

a =1 , b = 5 , c = 6

The roots of quadratic equation are given as follows:

x = (-b ± √ (b^2 - 4ac) )/2a.

x = (-5 ±√([tex]5^2[/tex]- 4(1)(6)) / 2 ×1

x = -5 ± 1/2

x = -2 , -3

Hence, The solution of the given quadratic equation [tex]x^{2} +5x+6[/tex] = 0 is x = -2 and -3

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well, the charge for a year is just 5.5% of the amount so 5.5% of 125000

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{5.5\% of 125000}}{\left( \cfrac{5.5}{100} \right)125000}\implies \text{\LARGE 6875}[/tex]

The solution to -4.5 x (-2) is 9.

What is the arithmetic calculation?

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.

The reason for this is that when two negative numbers are multiplied together, the result is positive.

This is because the negative sign on a number is similar to a "minus" sign, indicating that the number is less than zero.

When you have two "minus" signs together (in this case, one on -4.5 and one on -2),

they cancel each other out, leaving the positive product of 4.5 and 2, which is 9.

-4.5 is a negative decimal number, and -2 is also a negative integer number. When multiplied, it results in a positive number, which is 9.

Hence, the solution to -4.5 x (-2) is 9.

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Answer:

42

Step-by-step explanation:

18/3 = 6

6*7 =42

The lettered measurements for angles or sides in descending order is a, b, c.

When a pattern of numbers in mathematics has a decreasing value, the numbers are said to be in descending order. It indicates that the numbers are sorted from highest to lowest.

A format where items are arranged from highest to lowest is known as descending order. These ideas have to do with money, fractions, decimals, and numbers.

In right triangle, the sides facing the acute angles are opposite to the angles. From the given triangle, you can see that:

Side "b" is facing angle 50°

Side "c" is the smallest side which facing the unknown angle (40°)

the third side is largest side of right triangle facing the angle 90°. this is the smallest side of second triangle because of side opposite to smallest angle.

Side "a" is facing the unknown angle of second triangle (100°)

So the correct descending order is a, b, c.

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The given lengths (A) 18,10,6; (B) 6,2,8; (C) 8,10,15; and (D) 8,12,20 can be possible lengths of a triangle.

The length of the sides of a triangle are known as its dimensions. The sum of any two sides must be greater than the third side. That is, the sum of any two sides must be greater than the remaining side. This is known as the Triangle Inequality Theorem.

Let us consider the four possible combinations of lengths given in the question:

A) 18,10,6

The sum of any two sides must be greater than the remaining side.

18 + 10 = 28 > 6

10 + 6 = 16 > 18

6 + 18 = 24 > 10

Hence, this is a valid triangle.

B) 6,2,8

The sum of any two sides must be greater than the remaining side.

6 + 2 = 8 > 8

2 + 8 = 10 > 6

8 + 6 = 14 > 2

Hence, this is a valid triangle.

C) 8,10,15

The sum of any two sides must be greater than the remaining side.

8 + 10 = 18 > 15

10 + 15 = 25 > 8

15 + 8 = 23 > 10

Hence, this is a valid triangle.

D) 8,12,20

The sum of any two sides must be greater than the remaining side.

8 + 12 = 20 > 20

12 + 20 = 32 > 8

20 + 8 = 28 > 12

Hence, this is a valid triangle.

Therefore, all of the given lengths (A) 18,10,6; (B) 6,2,8; (C) 8,10,15; and (D) 8,12,20 can be possible lengths of a triangle.

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Answer: 5$ took test

Step-by-step explanation:

Answer:

Step-by-step explanation:

5 is the answer

Answer: $2,704.00

Step-by-step explanation:

First, convert R as a percent to r as a decimal

r = R/100

r = 4/100

r = 0.04 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 2,500.00(1 + 0.04/1)(1)(2)

A = 2,500.00(1 + 0.04)(2)

A = $2,704.00

Summary:

The total amount accrued, principal plus interest, with compound interest on a principal of $2,500.00 at a rate of 4% per year compounded 1 times per year over 2 years is $2,704.00.

The Initial value is computed at: 190

The Growth Factor is computed at: 0.5

A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth. When the input variable x appears as an exponent in the formula f(x) = axe, an exponential function is indicated. The exponential curve is influenced by both the exponential function and the value of x.

Given: Q = 190 / 2t

To compute: If [tex]Q = ab^t}[/tex]

Then,

→ 1 / aˣ = (1 / a)ˣ

Now we know that:

∵ (1 / aˣ) = (1 / a)ˣ

⇒ Q = 190 / 2t = 190 * (1 / 2t)

⇒ Q = 190 * (1 / 2)

[tex]Q = 190 * (\frac{1}{2})^{t}[/tex]

[tex]Q = 190 * (0.5)^{t}[/tex]

Comparing the aforementioned expression to:

[tex]Q = ab^{t}[/tex]

Initial Value, a = 190

Growth Factor, b = 0.5

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The equation of a line that passes through the point (2, 3) and (4, 7) is y = 2x - 1.

In the given question, we have to find the equation of a line that passes through the point (2, 3) and (4, 7).

The general equation of line that passes through point is:

y - y(1) = m(x - x(1))

To find the equation of line we have to first find the slope of line by using the formula:

m = [tex]\frac{y(2)-y(1)}{x(2)-x(1)}[/tex]

The given points:

(x(1), y(1)) = (2, 3), (x(2), y(2)) = (4, 7)

m = [tex]\frac{7-3}{4-2}[/tex]

m = [tex]\frac{4}{2}[/tex]

m = 2

Now finding the line of equation.

We can use any of the point of the given.

m = 2, (x(1), y(1)) = (2, 3)

y - 3 = 2(x - 2)

Solving the equation using distributive property

y - 3 = 2x - 4

Add 3 on both side, we get

y = 2x - 1

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The complete question is:

What is the equation of a line that passes through the point (2, 3) and (4, 7)?

Answer:

C 40m + 0.73

Step-by-step explanation:

since it is 40 per month it would be 40m because the m stands for how many months the chocolate factory charges for delivery and the extra .73 for every chocolate bar is an add on which would make this 40m + 0.73

The function that represent reflection of f(x) is given by g(x) = Negative two-fifths(10)x

Similar to reflections regarding the y-axis, the x-axis reflections are fundamentally the same. The only distinction is that the points are mirrored from above the x-axis to below the x-axis, and vice versa, rather than along the y-axis.

Make sure you have studied how to perform basic vertical and horizontal translations before we move on to reflections across the y-axis.

The reflection across the co-ordinate axis which is x-axis is as follows;

Reflection about the x-axis

Pre-image point before reflection = (x, y)

Point of image after reflection = ((x, -y)

Therefore, the x coordinate remains the same while the y coordinate changes sign

For which given that f(x) = y = 2/5(10)x and g(x) = Reflection of f(x) across the x-axis, we have

Reflection about the x-axis

Pre-image point before reflection = (x, f(x))

cordinate of image after the reflection = (x, g(x))

Hence g(x) = -f(x) = -2/5(10)x.

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Complete question:

Which function represents g(x), a reflection of f(x) = Two-fifths (10)x across the x-axis? g(x) = Negative two-fifths(10)x g(x) = Negative two-fifths (one-tenth) Superscript x g(x) = Two-fifths (one-tenth) Superscript negative x g(x) = Two-fifths(10)-x

Answer:

Step-by-step explanation:

We can begin to solve this problem using mathematics. Let's name the total sales for the month "S".

We know that the salesman receives a 10% commission on sales over $300,000 and a 12% commission on sales above 500,000. As a result, we may construct the following equation:

Commission = 0.10 (S - 300,000) + 0.12 (S - 500,000) = 0.10 (S - 30,000) + 0.12 (S - 60,000) = 0.22 (S - 90,000).

We also know that the salesman receives a total commission of $13,900. So we can plug that number into the equation:

13,900 = 0.22S - 90,000

To obtain the value of S, multiply both sides of the equation by 90,000:

13,900 + 90,000 = 0.22S

103,900 = 0.22S

Finally, we can obtain the value of S by dividing both sides of the equation by 0.22: S = 472,273.63

As a result, the total sales for the month were Sh 472,273.63.

Answer: 1/10 is literally only one out of 10. the fraction to a decimal is 0.1 so, 3 x 0.1 is 0.3 and 3 x 10 is 30.

0.3 is less than 30.

Step-by-step explanation:

The solution to the complex number (-5 - i)/(-6 - 9i) is (1 - i)/3

An equation shows the relationship between numbers and variables in an expression.

Complex numbers are in the form a + bi, where both a and b are real numbers and i = √(-1)

Given that:

[tex]\frac{-5-i}{-6-9i} \\\\To\ solve\ multiply\ numerator\ and\ denominator\ by\ conjugate:\\\\=\frac{-5-i}{-6-9i} *\frac{-6+9i}{-6+9i}\\ \\=\frac{30-45i+6i+9}{36+81}\\ \\=\frac{39-39i}{117} \\\\=\frac{1-i}{3}[/tex]

The solution is (1 - i)/3

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The given expression at a = 9 and b = 8 is equivalent to 71.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is the mathematical expression as -

{b + 7a}

Given is the expression as -

{b + 7a}

For a = 9 and b = 8, we can write -

{b + 7a}

{8 + 7 x 9}

{8 + 63}

71

Therefore, the given expression at a = 9 and b = 8 is equivalent to 71.

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{The complete question is -

evaluate the expression when a = 9 and b = 8 :

b + 7a}

[tex]\qquad \qquad \textit{binomial theorem expansion} \\\\ \qquad \qquad (3-5z)^{14}~\hspace{4em} \begin{array}{clcl} term&coefficient&value\\ \cline{1-3}&\\ 1&+1&(3)^{14 }(-5z)^0\\ 2&+14&(3)^{13}(-5z)^1\\ 3&+91&(3)^{12}(-5z)^2\\ 4&+364&(3)^{11}(-5z)^3\\ 5&+1001&(3)^{10}(-5z)^4 \end{array} \\\\[-0.35em] ~\dotfill\\\\ 3^{14}-14(3^{13})(5z)+91(3^{12})(5z)^2-364(3^{11})(5z)^3+1001(3^{10})(5z)^4 \\\\\\ 4782969-111602610z+1209028275z^2-8060188500z^3+13299311025z^4[/tex]

I find the key to binomial expansion is mainly to get coefficient that goes next as  you see in the middle of the table above.

now, if wonder how I get it sequentially, namely as I go, for example, how did I get 91?  

well, (14 * 13 )/ 2

the current coeffient times the exponent of the 1st term divided by the "exponent of the 2nd term plus 1"

how did I get 1001?

well, (364 * 11) / 4

and so on.